'''simple docstring'''




from __future__ import annotations

import math






def __lowerCAmelCase					(				UpperCamelCase__							)      ->       bool:

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5							,    int(math.sqrt(UpperCamelCase__							) + 1							)							,    6							):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True






def __lowerCAmelCase					(				UpperCamelCase__							)      ->       list[int]:
    __lowerCamelCase            =    str(UpperCamelCase__							)
    __lowerCamelCase            =    [n]
    for i in range(1							,    len(UpperCamelCase__							)							):
        list_nums.append(int(str_num[i:]							)							)
        list_nums.append(int(str_num[:-i]							)							)
    return list_nums






def __lowerCAmelCase					(				UpperCamelCase__							)      ->       bool:
    if len(str(UpperCamelCase__							)							) > 3:
        if not is_prime(int(str(UpperCamelCase__							)[-3:]							)							) or not is_prime(int(str(UpperCamelCase__							)[:3]							)							):
            return False
    return True






def __lowerCAmelCase					(				UpperCamelCase__ = 11							)      ->       list[int]:
    __lowerCamelCase            =    []
    __lowerCamelCase            =    13
    while len(UpperCamelCase__							) != count:
        if validate(UpperCamelCase__							):
            __lowerCamelCase            =    list_truncated_nums(UpperCamelCase__							)
            if all(is_prime(UpperCamelCase__							) for i in list_nums							):
                list_truncated_primes.append(UpperCamelCase__							)
        num += 2
    return list_truncated_primes






def __lowerCAmelCase					(				)      ->       int:
    return sum(compute_truncated_primes(11							)							)


if __name__ == "__main__":
  print(f'{sum(compute_truncated_primes(1_1)) = }')

'''simple docstring'''




import numpy as np






def __lowerCAmelCase					(				UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							,    UpperCamelCase__							)      ->       str:
    __lowerCamelCase            =    int(np.ceil((x_end - xa) / h							)							)
    __lowerCamelCase            =    np.zeros((n + 1,)							)
    __lowerCamelCase            =    ya
    __lowerCamelCase            =    xa

    for k in range(UpperCamelCase__							):
        __lowerCamelCase            =    f(UpperCamelCase__							,    y[k]							)
        __lowerCamelCase            =    f(x + 0.5 * h							,    y[k] + 0.5 * h * ka							)
        __lowerCamelCase            =    f(x + 0.5 * h							,    y[k] + 0.5 * h * ka							)
        __lowerCamelCase            =    f(x + h							,    y[k] + h * ka							)
        __lowerCamelCase            =    y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
        x += h

    return y


if __name__ == "__main__":
  import doctest

  doctest.testmod()
